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Prisms and Diffractive Optics

PrismsTunnel diagrams uses of different types

GRIN lenses Diffractive optics

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PrismsWhat are they good for?

Fold- Erect or rotate images- Change direction of propagation- Displace the beam- Fold system for compactness

Retro-reflection Disperse (vs. ) Control beam parameters

Anamorphic telescopes Vary angle, position, path length

Amplitude or pol. division Beam splitters

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Folding prismsBouncing pencils to analyze image orientation

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What the rotations are called

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Folding prismsBouncing pencils to analyze image orientation

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Tunnel diagramsTool to simplify ray-tracing

Unfold the path and squash the dimensions by n: useful to determine the angular field of the prism as well as the size of the beam which will pass, and see what aberration might it cause.

Dove Prism is equivalent to a tilted plane of glass. Will have lots of astigmatism if used in converging or diverging beam

Right angle prism equivalent to block of glass

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Tunnel diagramsTool to simplify ray-tracing

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More Complex Example

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3D Tunnel diagramsTool to simplify ray-tracing

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Anamorphic prismsOften better than cylindrical telescope

Problems: Compression largest near TIR tolerances and polarization dependence

Angular bandwidth quite low (works best for collimated beams)

Advantages Lower aberrations than cylinders

Cheap

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Prism Deviation of Ray

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Thin PrismUse paraxial approximation

When A is small angle and light incident near normal to prism face thin prism

Which gives:

Differentiate with respect to n results in

VD

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Thin prism tricksBeam is deviated by angle (n-1)a. If prismis rotated about its axis, the beam isdeflected in a circle. Two cascaded prismsgive arbitrary x,y deviation. For small a,control of deviation can be quite fine.

As above, if is small, control ofdisplacement can be quite fine.

Variable path length.

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GRIN lensesCommon in fiber/telecom applications

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GRIN lenses Good example and important lens technolgy

Standard Lens increases the OPL in the middle and decreases towards edges by change in thickness of the glass.

fyxjko

eyxt 222

),(+

What if index of plane of glass d0 thick varies radially as no(1-1/22)(x2+y2) ?

The transmittance can be written as (ignore constant phase terms)

2)( 222

),(yxndkj ooo

eyxt+

This gives a focus length

oo dnf 2

1

=

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Classes Diffractive optical element: Modification of the optical wavefront via subdivision and individual modification of the phase and/or amplitude of the segments. Grating: linear segments = uniform diffraction angle Computer generated hologram: A DOE in which the structure has been calculated numericallyHolographic optical element: DOE in which the structure is generated by the interference of optical wavefronts.DiscretizationBinary optic: phase or amplitude structure with two levels. Typically created via a single etch step. Dammann grating: Binary optics with repetitive pattern, generates N beams (fan out) Multilevel optic: Same as binary but with M etch steps to achieve N=2M levels. Kinoform: Phase DOE with smoothly varying profile (limit of N) Blazed: Grating with linear (sawtooth) segmentsFabrication Direct machining: aka ruling or diamond turning, fab via mechanical machining. Often used for masters. Lithography Direct write: scan laser or e-beam over photoresist Interference (holography) inc near field Masks: grey-scale, multiple exposure Replication

Diffractive opticsIntroduction/terminology

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Diffraction gratingsBasics

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Diffraction gratingsBasics

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Resolving poweraka number of spots

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Resolving poweraka number of spots

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Estimation of grating RWhy gratings are interesting

Holographic gratings of 1800 lp/mm are typical in the visible. A 10 mm beam and first-order diffraction would yield

R = 10 1800 = 18,000or a minimum resolvable wavelength shift of 0.03 nm in the visible.For a prism at the minimum deviation condition (symmetrical incident and exit angles) the resolving power can be shown to be

In the visible a b = 25 mm prism would give resolving power

or ~ 0.5 to 0.17 nm, roughly an order of magnitude lower resolution than a grating.

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When will diffractions be confused with the neighboring order?

Bandwidthaka Free spectral range

Thus first-order grating spectrometer could operate from 400 to 800 nm.

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EfficiencyOverview by type

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EfficiencyOverview by type

Thick phase grating: Bragg selectivity can give single order and theoretically 100% DE. BUT, very sensitive to incident wavelength and/or angle (unlike thin).

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Multilevel DOEsWhy you pay for them

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Multilevel DOEsWhy you pay for them

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Diffractive lens designMultilevel on-axis Fresnel

What is the radial location of the pth zone for a mth order DOE fabricated with N layer?

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Diffractive lens designMultilevel on-axis Fresnel

Note for minimum feature size, N reduces F/# linearly (ouch).

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Diffractive lenses dependence of angles

Reading a diffractive optic at and order m that was designed for and order m.

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Diffractive lenses dependence of angles

Reading a diffractive optic at and order m that was designed for and order m.

Change in angle is perfectly analogous torefracting into a slab of index neff. Notethat this index can be < 1.

Definition of focal length.1. Diffracts to set of focii.2. For neff1, each suffers spherical aberration.

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Diffractive lenses dependence of efficiency (1/4)

For a kinoform (N= )

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Diffractive lenses dependence of efficiency (2/4)

Which gives us the diffracted electric field vs. angle for a uniform Einc

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Diffractive lenses dependence of efficiency (3/4)

Efficiency of a blazed grating designed for wavelength and order m with index n read at wavelength l and order m with index n

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Diffractive lenses dependence of efficiency (4/4)

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Hybrid refractive/DOEsFrom earlier

If used at same order (m=m)

Find change in power over l

From earlier

Solve for V.

This is a) the same for all DOEs, b) negative and c) very strong.Lets design an achromatic f=25.4 mm with a BK7 singlet:

For DOE

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Hybrid Continued

In Zemax, thin DOEs are usually modeled with infinitely thin surface with extremely large index perturbations ie 10,000 at design wavelength and index scaling with wavelength

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Reading

W. Smith Modern Optical Engineering

Chapter 7